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    <title>wiener</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>wiener</b> -   Wiener estimate</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[xs,ps,xf,pf]=wiener(y,x0,p0,f,g,h,q,r)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>f, g, h</b>
        </tt>: system matrices in the interval <tt>
          <b>[t0,tf]</b>
        </tt>
        <ul>
          <li>
            <tt>
              <b>f</b>
            </tt>=<tt>
              <b>[f0,f1,...,ff]</b>
            </tt>, and <tt>
              <b>fk</b>
            </tt> is a nxn matrix</li>
          <li>
            <tt>
              <b>g</b>
            </tt>=<tt>
              <b>[g0,g1,...,gf]</b>
            </tt>, and <tt>
              <b>gk</b>
            </tt> is a nxn matrix</li>
          <li>
            <tt>
              <b>h</b>
            </tt>=<tt>
              <b>[h0,h1,...,hf]</b>
            </tt>, and <tt>
              <b>hk</b>
            </tt> is a mxn matrix</li>
        </ul>
      </li>
      <li>
        <tt>
          <b>q, r</b>
        </tt>: covariance matrices of dynamics and observation noise<ul>
          <li>
            <tt>
              <b>q</b>
            </tt>=<tt>
              <b>[q0,q1,...,qf]</b>
            </tt>, and <tt>
              <b>qk</b>
            </tt> is a nxn matrix</li>
          <li>
            <tt>
              <b>r</b>
            </tt>=<tt>
              <b>[r0,r1,...,rf]</b>
            </tt>, and <tt>
              <b>gk</b>
            </tt> is a mxm matrix</li>
        </ul>
      </li>
      <li>
        <tt>
          <b>x0, p0</b>
        </tt>: initial state estimate and error variance</li>
      <li>
        <tt>
          <b>y</b>
        </tt>: observations in the interval <tt>
          <b>[t0,tf]</b>
        </tt>. <tt>
          <b>y=[y0,y1,...,yf]</b>
        </tt>, and <tt>
          <b>yk</b>
        </tt> is a column m-vector</li>
      <li>
        <tt>
          <b>xs</b>
        </tt>: Smoothed state estimate <tt>
          <b>xs= [xs0,xs1,...,xsf]</b>
        </tt>, and <tt>
          <b>xsk</b>
        </tt> is a column n-vector</li>
      <li>
        <tt>
          <b>ps</b>
        </tt>: Error covariance of smoothed estimate <tt>
          <b>ps=[p0,p1,...,pf]</b>
        </tt>, and <tt>
          <b>pk</b>
        </tt> is a nxn matrix</li>
      <li>
        <tt>
          <b>xf</b>
        </tt>: Filtered state estimate <tt>
          <b>xf= [xf0,xf1,...,xff]</b>
        </tt>, and <tt>
          <b>xfk</b>
        </tt> is a column n-vector</li>
      <li>
        <tt>
          <b>pf</b>
        </tt>: Error covariance of filtered estimate <tt>
          <b>pf=[p0,p1,...,pf]</b>
        </tt>, and <tt>
          <b>pk</b>
        </tt> is a nxn matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    function which gives the Wiener estimate using
    the forward-backward Kalman filter formulation</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>C. B.  </p>
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